Physics Letters B 751 (2015) 29–33
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Gravitational mass of relativistic matter and antimatter
Tigran Kalaydzhyan
a,b,∗
a
Department of Physics, University of Illinois, Chicago, IL 60607-7059, USA
b
Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received
11 August 2015
Received
in revised form 10 September
2015
Accepted
6 October 2015
Available
online 13 October 2015
Editor:
A. Ringwald
The universality of free fall, the weak equivalence principle (WEP), is a cornerstone of the general theory
of relativity, the most precise theory of gravity confirmed in all experiments up to date. The WEP
states the equivalence of the inertial, m, and gravitational, m
g
, masses and was tested in numerous
occasions with normal matter at relatively low energies. However, there is no confirmation for the
matter and antimatter at high energies. For the antimatter the situation is even less clear – current
direct observations of trapped antihydrogen suggest the limits −65 < m
g
/m < 110 not excluding the so-
called
antigravity phenomenon, i.e. repulsion of the antimatter by Earth. Here we demonstrate an indirect
bound 0.96 < m
g
/m < 1.04 on the gravitational mass of relativistic electrons and positrons coming from
the absence of the vacuum Cherenkov radiation at the Large Electron–Positron Collider (LEP) and stability
of photons at the Tevatron collider in presence of the annual variations of the solar gravitational potential.
Our result clearly rules out the speculated antigravity. By considering the absolute potential of the Local
Supercluster (LS), we also predict the bounds 1 − 4 × 10
−7
< m
g
/m < 1 + 2 × 10
−7
for an electron
and positron. Finally, we comment on a possibility of performing complementary tests at the future
International Linear Collider (ILC) and Compact Linear Collider (CLIC).
© 2015 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Since the formulation of the general relativity (GR) by Einstein
in 1915–1916 [1,2] there were numerous tests confirming validity
of the theory with an exceptional precision [3]. The weak equiva-
lence
principle (WEP), postulating the universality of the free fall,
or equivalence of the inertial and gravitational masses, was con-
firmed
in torsion balance experiments [4] at the 2 × 10
−13
level
for the normal matter. The idea of “antigravity” for an exotic mat-
ter
seems to exist since the end of the XIX century [5], where it
appeared together with the idea of antimatter. The modern, quan-
tum,
concept of antimatter begins with the theoretical paper of
Dirac [6] in 1928 and experimental observation of antielectron
(positron) by Anderson [7] in 1933. However, since then, there is
no conclusion made about the gravitational interaction of antimat-
ter [8].
The most precise direct observation of cold-trapped antihy-
drogen [9] sets
the limits on the ratio between the inertial m and
gravitational m
g
masses of the antihydrogen, −65 < m
g
/m < 110,
including systematic errors, at the 5% significance level [9]. At the
*
Correspondence to: Department of Physics, University of Illinois, Chicago, IL
60607-7059, USA.
E-mail
address: tigran@uic.edu.
same time, indirect limits have a long history and are much stricter
(even though, most of them use additional assumptions), see re-
view [10] for
the arguments prior to 1991. At the moment, the
most precise bounds on the difference between the gravitational
masses of the matter and antimatter (to our knowledge) are ob-
tained
from the comparison of decay parameters of the K
0
–
¯
K
0
system [11] (1.8 × 10
−9
level with gravitational potential varia-
tions
and 1.9 × 10
−14
with the LS potential) and from comparison
of cyclotron frequencies [12] of the p–
¯
p system [13] (10
−6
level
with LS potential). Equality of the inertial masses for the con-
sidered
(anti)particles is supported by the CP T -symmetry tested
with a much higher precision [14]. These and other indirect lim-
its
are, however, not absolute, but relative (between particles and
antiparticles) and for relatively low energies. There is, therefore,
no guarantee that, e.g., the strange matter (kaons) at any ener-
gies,
or normal matter and antimatter at high energies (several
GeV and higher) will obey WEP. These limits also do not restrict
certain WEP violation models, such as the “isotropic parachute
model” [15].
Even
though astrophysical tests of the Lorentz invariance
[16–19] can be, perhaps, used for the precise tests of the WEP
(mainly for electrons and protons), they rely on certain mod-
els
describing the high-energy sources and their dynamics. It is,
http://dx.doi.org/10.1016/j.physletb.2015.10.014
0370-2693/
© 2015 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.